A035290 Number of ways to place a non-attacking white and black pawn on n X n chessboard.

0, 0, 6, 50, 194, 522, 1142, 2186, 3810, 6194, 9542, 14082, 20066, 27770, 37494, 49562, 64322, 82146, 103430, 128594, 158082, 192362, 231926, 277290, 328994, 387602, 453702, 527906, 610850, 703194, 805622, 918842, 1043586, 1180610

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n^4 - 4 n^3 + n^2 + 10 n - 6.

G.f.: -2*x^3*(x+1)*(x^3-5*x^2+7*x+3)/(x-1)^5. [Colin Barker, Jan 09 2013]

Example

There are 6 ways of putting 1 white and 1 black pawn on 3 X 3 so that neither can capture the other. pawns can't be on first or last rank.

Mathematica

CoefficientList[Series[- 2 x^2 (x + 1) (x^3 - 5 x^2 + 7 x + 3)/(x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 20 2013 *)

Prog

(Magma) [n le 2 select 0 else n^4-4*n^3+n^2+10*n-6: n in [1..50]]; // Vincenzo Librandi, Oct 20 2013

Crossrefs

Sequence in context: A187462 A231270 A062801 * A138422 A356251 A001303

Adjacent sequences: A035287 A035288 A035289 * A035291 A035292 A035293

Keyword

nonn,easy

Author

Erich Friedman

Status

approved